Multiplying Binomials Worksheet | PDF Printable Algebra Worksheet - Free Printable

Let's solve each problem in Section A and Section B by expanding the binomials using the FOIL method (First, Outer, Inner, Last), then simplifying by combining like terms.

---

🔷 Section A: Multiply and Simplify

We'll go through each one step-by-step.

---

#### 1) $ (x + 2)(x + 7) $

- First: $ x \cdot x = x^2 $
- Outer: $ x \cdot 7 = 7x $
- Inner: $ 2 \cdot x = 2x $
- Last: $ 2 \cdot 7 = 14 $

Add:
$ x^2 + 7x + 2x + 14 = x^2 + 9x + 14 $

✔ Answer: $ x^2 + 9x + 14 $

---

#### 2) $ (x + 9)(x + 5) $

- First: $ x \cdot x = x^2 $
- Outer: $ x \cdot 5 = 5x $
- Inner: $ 9 \cdot x = 9x $
- Last: $ 9 \cdot 5 = 45 $

Add:
$ x^2 + 5x + 9x + 45 = x^2 + 14x + 45 $

✔ Answer: $ x^2 + 14x + 45 $

---

#### 3) $ (x - 8)(x + 1) $

- First: $ x \cdot x = x^2 $
- Outer: $ x \cdot 1 = x $
- Inner: $ -8 \cdot x = -8x $
- Last: $ -8 \cdot 1 = -8 $

Add:
$ x^2 + x - 8x - 8 = x^2 - 7x - 8 $

✔ Answer: $ x^2 - 7x - 8 $

---

#### 4) $ (x - 3)(x - 4) $

- First: $ x \cdot x = x^2 $
- Outer: $ x \cdot (-4) = -4x $
- Inner: $ -3 \cdot x = -3x $
- Last: $ -3 \cdot (-4) = 12 $

Add:
$ x^2 - 4x - 3x + 12 = x^2 - 7x + 12 $

✔ Answer: $ x^2 - 7x + 12 $

---

#### 5) $ (8x + 10)(x + 3) $

- First: $ 8x \cdot x = 8x^2 $
- Outer: $ 8x \cdot 3 = 24x $
- Inner: $ 10 \cdot x = 10x $
- Last: $ 10 \cdot 3 = 30 $

Add:
$ 8x^2 + 24x + 10x + 30 = 8x^2 + 34x + 30 $

✔ Answer: $ 8x^2 + 34x + 30 $

---

#### 6) $ (2x + 11)(9x + 2) $

- First: $ 2x \cdot 9x = 18x^2 $
- Outer: $ 2x \cdot 2 = 4x $
- Inner: $ 11 \cdot 9x = 99x $
- Last: $ 11 \cdot 2 = 22 $

Add:
$ 18x^2 + 4x + 99x + 22 = 18x^2 + 103x + 22 $

✔ Answer: $ 18x^2 + 103x + 22 $

---

#### 7) $ (5x - 4)(x + 3) $

- First: $ 5x \cdot x = 5x^2 $
- Outer: $ 5x \cdot 3 = 15x $
- Inner: $ -4 \cdot x = -4x $
- Last: $ -4 \cdot 3 = -12 $

Add:
$ 5x^2 + 15x - 4x - 12 = 5x^2 + 11x - 12 $

✔ Answer: $ 5x^2 + 11x - 12 $

---

#### 8) $ (3x + 1)(x - 2) $

- First: $ 3x \cdot x = 3x^2 $
- Outer: $ 3x \cdot (-2) = -6x $
- Inner: $ 1 \cdot x = x $
- Last: $ 1 \cdot (-2) = -2 $

Add:
$ 3x^2 - 6x + x - 2 = 3x^2 - 5x - 2 $

✔ Answer: $ 3x^2 - 5x - 2 $

---

#### 9) $ (7x - 4)(4x - 5) $

- First: $ 7x \cdot 4x = 28x^2 $
- Outer: $ 7x \cdot (-5) = -35x $
- Inner: $ -4 \cdot 4x = -16x $
- Last: $ -4 \cdot (-5) = 20 $

Add:
$ 28x^2 - 35x - 16x + 20 = 28x^2 - 51x + 20 $

✔ Answer: $ 28x^2 - 51x + 20 $

---

#### 10) $ (6x - 1)(4x + 3) $

- First: $ 6x \cdot 4x = 24x^2 $
- Outer: $ 6x \cdot 3 = 18x $
- Inner: $ -1 \cdot 4x = -4x $
- Last: $ -1 \cdot 3 = -3 $

Add:
$ 24x^2 + 18x - 4x - 3 = 24x^2 + 14x - 3 $

✔ Answer: $ 24x^2 + 14x - 3 $

---

#### 11) $ (8x - 3)(4x + 1) $

- First: $ 8x \cdot 4x = 32x^2 $
- Outer: $ 8x \cdot 1 = 8x $
- Inner: $ -3 \cdot 4x = -12x $
- Last: $ -3 \cdot 1 = -3 $

Add:
$ 32x^2 + 8x - 12x - 3 = 32x^2 - 4x - 3 $

✔ Answer: $ 32x^2 - 4x - 3 $

---

#### 12) $ (2x - 6)(3x - 5) $

- First: $ 2x \cdot 3x = 6x^2 $
- Outer: $ 2x \cdot (-5) = -10x $
- Inner: $ -6 \cdot 3x = -18x $
- Last: $ -6 \cdot (-5) = 30 $

Add:
$ 6x^2 - 10x - 18x + 30 = 6x^2 - 28x + 30 $

✔ Answer: $ 6x^2 - 28x + 30 $

---

#### 13) $ (2x - 6)(3x - 5) $ ← Same as #12

✔ Answer: $ 6x^2 - 28x + 30 $

*(Note: This is a duplicate of #12.)*

---

#### 14) $ (6 - x)(x - 7) $

Rewriting: $ (-x + 6)(x - 7) $

- First: $ -x \cdot x = -x^2 $
- Outer: $ -x \cdot (-7) = 7x $
- Inner: $ 6 \cdot x = 6x $
- Last: $ 6 \cdot (-7) = -42 $

Add:
$ -x^2 + 7x + 6x - 42 = -x^2 + 13x - 42 $

✔ Answer: $ -x^2 + 13x - 42 $

---

#### 15) $ (3 - 2x)(2 - x) $

Rewriting: $ (-2x + 3)(-x + 2) $

- First: $ -2x \cdot (-x) = 2x^2 $
- Outer: $ -2x \cdot 2 = -4x $
- Inner: $ 3 \cdot (-x) = -3x $
- Last: $ 3 \cdot 2 = 6 $

Add:
$ 2x^2 - 4x - 3x + 6 = 2x^2 - 7x + 6 $

✔ Answer: $ 2x^2 - 7x + 6 $

---

🔷 Section B: Multiply and Simplify

Now we work with variables $ a $ and $ b $. Use FOIL again.

---

#### 1) $ (a + b)(a + b) $

This is $ (a + b)^2 $

- First: $ a \cdot a = a^2 $
- Outer: $ a \cdot b = ab $
- Inner: $ b \cdot a = ab $
- Last: $ b \cdot b = b^2 $

Add:
$ a^2 + ab + ab + b^2 = a^2 + 2ab + b^2 $

✔ Answer: $ a^2 + 2ab + b^2 $

---

#### 2) $ (3a + b)(2a + b) $

- First: $ 3a \cdot 2a = 6a^2 $
- Outer: $ 3a \cdot b = 3ab $
- Inner: $ b \cdot 2a = 2ab $
- Last: $ b \cdot b = b^2 $

Add:
$ 6a^2 + 3ab + 2ab + b^2 = 6a^2 + 5ab + b^2 $

✔ Answer: $ 6a^2 + 5ab + b^2 $

---

#### 3) $ (5a + 2b)(a + b) $

- First: $ 5a \cdot a = 5a^2 $
- Outer: $ 5a \cdot b = 5ab $
- Inner: $ 2b \cdot a = 2ab $
- Last: $ 2b \cdot b = 2b^2 $

Add:
$ 5a^2 + 5ab + 2ab + 2b^2 = 5a^2 + 7ab + 2b^2 $

✔ Answer: $ 5a^2 + 7ab + 2b^2 $

---

#### 4) $ (4a + b)(5a + 2b) $

- First: $ 4a \cdot 5a = 20a^2 $
- Outer: $ 4a \cdot 2b = 8ab $
- Inner: $ b \cdot 5a = 5ab $
- Last: $ b \cdot 2b = 2b^2 $

Add:
$ 20a^2 + 8ab + 5ab + 2b^2 = 20a^2 + 13ab + 2b^2 $

✔ Answer: $ 20a^2 + 13ab + 2b^2 $

---

#### 5) $ (6a + 3b)(2a - b) $

- First: $ 6a \cdot 2a = 12a^2 $
- Outer: $ 6a \cdot (-b) = -6ab $
- Inner: $ 3b \cdot 2a = 6ab $
- Last: $ 3b \cdot (-b) = -3b^2 $

Add:
$ 12a^2 - 6ab + 6ab - 3b^2 = 12a^2 - 3b^2 $

✔ Answer: $ 12a^2 - 3b^2 $

---

#### 6) $ (7a - 5b)(a + 4b) $

- First: $ 7a \cdot a = 7a^2 $
- Outer: $ 7a \cdot 4b = 28ab $
- Inner: $ -5b \cdot a = -5ab $
- Last: $ -5b \cdot 4b = -20b^2 $

Add:
$ 7a^2 + 28ab - 5ab - 20b^2 = 7a^2 + 23ab - 20b^2 $

✔ Answer: $ 7a^2 + 23ab - 20b^2 $

---

#### 7) $ (a - 3b)(11a - b) $

- First: $ a \cdot 11a = 11a^2 $
- Outer: $ a \cdot (-b) = -ab $
- Inner: $ -3b \cdot 11a = -33ab $
- Last: $ -3b \cdot (-b) = 3b^2 $

Add:
$ 11a^2 - ab - 33ab + 3b^2 = 11a^2 - 34ab + 3b^2 $

✔ Answer: $ 11a^2 - 34ab + 3b^2 $

---

#### 8) $ (4a + 5b)(6a - 9b) $

- First: $ 4a \cdot 6a = 24a^2 $
- Outer: $ 4a \cdot (-9b) = -36ab $
- Inner: $ 5b \cdot 6a = 30ab $
- Last: $ 5b \cdot (-9b) = -45b^2 $

Add:
$ 24a^2 - 36ab + 30ab - 45b^2 = 24a^2 - 6ab - 45b^2 $

✔ Answer: $ 24a^2 - 6ab - 45b^2 $

---

#### 9) $ (x + 6)^2 $

This is $ (x + 6)(x + 6) $

- First: $ x \cdot x = x^2 $
- Outer: $ x \cdot 6 = 6x $
- Inner: $ 6 \cdot x = 6x $
- Last: $ 6 \cdot 6 = 36 $

Add:
$ x^2 + 6x + 6x + 36 = x^2 + 12x + 36 $

✔ Answer: $ x^2 + 12x + 36 $

---

## ✔ Final Answers Summary:

Section A

1. $ x^2 + 9x + 14 $
2. $ x^2 + 14x + 45 $
3. $ x^2 - 7x - 8 $
4. $ x^2 - 7x + 12 $
5. $ 8x^2 + 34x + 30 $
6. $ 18x^2 + 103x + 22 $
7. $ 5x^2 + 11x - 12 $
8. $ 3x^2 - 5x - 2 $
9. $ 28x^2 - 51x + 20 $
10. $ 24x^2 + 14x - 3 $
11. $ 32x^2 - 4x - 3 $
12. $ 6x^2 - 28x + 30 $
13. $ 6x^2 - 28x + 30 $
14. $ -x^2 + 13x - 42 $
15. $ 2x^2 - 7x + 6 $

Section B

1. $ a^2 + 2ab + b^2 $
2. $ 6a^2 + 5ab + b^2 $
3. $ 5a^2 + 7ab + 2b^2 $
4. $ 20a^2 + 13ab + 2b^2 $
5. $ 12a^2 - 3b^2 $
6. $ 7a^2 + 23ab - 20b^2 $
7. $ 11a^2 - 34ab + 3b^2 $
8. $ 24a^2 - 6ab - 45b^2 $
9. $ x^2 + 12x + 36 $

---

Let me know if you'd like these explained further or formatted into a printable sheet!